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Positively N-expansive Homeomorphisms and the L-shadowing Property

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Abstract

We discuss further the dynamics of n-expansive homeomorphisms with the shadowing property, started in Carvalho and Cordeiro (J Differ Equ 261:3734–3755, 2016). The L-shadowing property is defined and the dynamics of n-expansive homeomorphisms with such property is explored. In particular, we prove that positively n-expansive homeomorphisms with the L-shadowing property can only be defined in finite metric spaces.

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Acknowledgements

Part of this work was developed while the first author was working at UFV-Brazil and the second author was at IMPA being supported by CNPq(Brazil).

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal de Minas Gerais - UFMG, Av. Antônio Carlos, 6627 - Campus Pampulha, Caixa Postal: 702, Belo Horizonte, MG, 31270-901, Brazil

    Bernardo Carvalho

  2. Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich, 8, 00-656, Warszawa, Poland

    Welington Cordeiro

Authors
  1. Bernardo Carvalho
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  2. Welington Cordeiro
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Correspondence to Bernardo Carvalho.

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Carvalho, B., Cordeiro, W. Positively N-expansive Homeomorphisms and the L-shadowing Property. J Dyn Diff Equat 31, 1005–1016 (2019). https://doi.org/10.1007/s10884-018-9698-3

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  • DOI: https://doi.org/10.1007/s10884-018-9698-3

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